If there is a web cam in Eretz Yisrael that is operating on Shabbat, am I permited to view the web cam while it is Shabbat in E"Y but stil Chol here in Chutz L’a’aretz?

One can not benefit from a Chilul Shabbat of a fellow Jew, therefore if the operation of a website or the camera includes breaking the laws of Shabbat – you can't view it in your place even though it's not yet Shabbat by you and if it is does not involve violating Shabbat prohibitions – it's permissible. The mere fact there is a camera operating on the website does not necessarily mean it involves Chilul Shabbat.